Problem: $\begin{cases} f(1)=-71 \\\\ f(n)=f(n-1)\cdot 4.2 \end{cases}$ Find an explicit formula for $f(n)$. $f(n)=$
Explanation: From the recursive formula, we can tell that the first term of the sequence is ${-71}$ and the common ratio is ${4.2}$. This is the explicit formula of the sequence: $f(n)= {-71}\cdot {4.2}^{{\,n-1}}$. Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.